Data-Driven Output Synchronization of Heterogeneous Multi-Agent Systems under False Data Injection Attacks

This paper investigates strategies for achieving optimal output synchronization of heterogeneous multi-agent systems in the presence of false data injection attacks. We formulate a performance index with an infinite time horizon using a zero-sum game framework, treating control input and false data injection attack input as two opposing players. Specifically, the control input's objective is to minimize the performance index, while the false data injection attack input aims to maximize it. Adhering to the optimality principle, we derive the optimal control policy, contingent upon the solution to a related algebraic Riccati equation. Moreover, we propose sufficient conditions that ensure the existence of a solution to the algebraic Riccati equation. Additionally, we have devised a data-driven reinforcement learning algorithm to seek the solution, and its convergence is assured. Furthermore, it has been demonstrated that the solution to this game corresponds to a Nash equilibrium point. Finally, the validity of the proposed methodology is substantiated through simulation results.